How do you differentiate y = log x^2?

We have to differentiate y=log x2

We know that

log xn= n log x

log x²= 2 log x-(i)

We have learnt that

dy/ dx (log x) = 1/x

Hence equation i becomes

dy / dx = 2 log x = 2 . 1/x = 2/x

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How do you differentiate y = log x²?